Homoclinic intersections for geodesic flows on convex spheres

Zhihong Xia, Pengfei Zhang

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper, we study some generic properties of the geodesic flows on a convex sphere. We prove that, C r generically (2 ≤ r ≤ ∞), every hyperbolic closed geodesic on S 2 admits some transverse homoclinic intersections.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages221-238
Number of pages18
DOIs
StatePublished - Jan 1 2017

Publication series

NameContemporary Mathematics
Volume698
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Fingerprint

Generic Property
Closed Geodesics
Geodesic Flow
Homoclinic
Transverse
Intersection

Keywords

  • Closed geodesic
  • Convex spheres
  • Elliptic geodesic
  • Geodesic flow
  • Hyperbolic geodesic
  • Nonlinearly stable
  • Prime-end compactification
  • Transverse homoclinic intersections

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Xia, Z., & Zhang, P. (2017). Homoclinic intersections for geodesic flows on convex spheres. In Contemporary Mathematics (pp. 221-238). (Contemporary Mathematics; Vol. 698). American Mathematical Society. https://doi.org/10.1090/conm/698/13980
Xia, Zhihong ; Zhang, Pengfei. / Homoclinic intersections for geodesic flows on convex spheres. Contemporary Mathematics. American Mathematical Society, 2017. pp. 221-238 (Contemporary Mathematics).
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Xia, Z & Zhang, P 2017, Homoclinic intersections for geodesic flows on convex spheres. in Contemporary Mathematics. Contemporary Mathematics, vol. 698, American Mathematical Society, pp. 221-238. https://doi.org/10.1090/conm/698/13980

Homoclinic intersections for geodesic flows on convex spheres. / Xia, Zhihong; Zhang, Pengfei.

Contemporary Mathematics. American Mathematical Society, 2017. p. 221-238 (Contemporary Mathematics; Vol. 698).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Xia Z, Zhang P. Homoclinic intersections for geodesic flows on convex spheres. In Contemporary Mathematics. American Mathematical Society. 2017. p. 221-238. (Contemporary Mathematics). https://doi.org/10.1090/conm/698/13980